Valid and efficient entanglement verification with finite copies of a quantum state
Abstract Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme’s validity via the probability that the signal comes from a separable state, offering...
| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2024-01-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-024-00810-3 |
| _version_ | 1797276400417243136 |
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| author | Paweł Cieśliński Jan Dziewior Lukas Knips Waldemar Kłobus Jasmin Meinecke Tomasz Paterek Harald Weinfurter Wiesław Laskowski |
| author_facet | Paweł Cieśliński Jan Dziewior Lukas Knips Waldemar Kłobus Jasmin Meinecke Tomasz Paterek Harald Weinfurter Wiesław Laskowski |
| author_sort | Paweł Cieśliński |
| collection | DOAJ |
| description | Abstract Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme’s validity via the probability that the signal comes from a separable state, offering a meaningful figure of merit for big datasets. Yet, with limited samples, avoiding experimental data misinterpretations requires considering not only the probabilities concerning separable states but also the probability that the signal came from an entangled state, i.e. the detection scheme’s efficiency. We demonstrate this explicitly and apply a general method to optimize both the validity and the efficiency in small data sets providing examples using at most 20 state copies. The method is based on an analytical model of finite statistics effects on correlation functions which takes into account both a Frequentist as well as a Bayesian approach and is applicable to arbitrary entanglement witnesses. |
| first_indexed | 2024-03-07T15:27:46Z |
| format | Article |
| id | doaj.art-6a9003ff78fc40b2ba00514713c6828a |
| institution | Directory Open Access Journal |
| issn | 2056-6387 |
| language | English |
| last_indexed | 2024-03-07T15:27:46Z |
| publishDate | 2024-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj.art-6a9003ff78fc40b2ba00514713c6828a2024-03-05T16:37:39ZengNature Portfolionpj Quantum Information2056-63872024-01-0110111010.1038/s41534-024-00810-3Valid and efficient entanglement verification with finite copies of a quantum statePaweł Cieśliński0Jan Dziewior1Lukas Knips2Waldemar Kłobus3Jasmin Meinecke4Tomasz Paterek5Harald Weinfurter6Wiesław Laskowski7Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics, and Informatics, University of GdańskMax Planck Institute for Quantum OpticsMax Planck Institute for Quantum OpticsInstitute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics, and Informatics, University of GdańskMax Planck Institute for Quantum OpticsInstitute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics, and Informatics, University of GdańskInstitute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics, and Informatics, University of GdańskInstitute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics, and Informatics, University of GdańskAbstract Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme’s validity via the probability that the signal comes from a separable state, offering a meaningful figure of merit for big datasets. Yet, with limited samples, avoiding experimental data misinterpretations requires considering not only the probabilities concerning separable states but also the probability that the signal came from an entangled state, i.e. the detection scheme’s efficiency. We demonstrate this explicitly and apply a general method to optimize both the validity and the efficiency in small data sets providing examples using at most 20 state copies. The method is based on an analytical model of finite statistics effects on correlation functions which takes into account both a Frequentist as well as a Bayesian approach and is applicable to arbitrary entanglement witnesses.https://doi.org/10.1038/s41534-024-00810-3 |
| spellingShingle | Paweł Cieśliński Jan Dziewior Lukas Knips Waldemar Kłobus Jasmin Meinecke Tomasz Paterek Harald Weinfurter Wiesław Laskowski Valid and efficient entanglement verification with finite copies of a quantum state npj Quantum Information |
| title | Valid and efficient entanglement verification with finite copies of a quantum state |
| title_full | Valid and efficient entanglement verification with finite copies of a quantum state |
| title_fullStr | Valid and efficient entanglement verification with finite copies of a quantum state |
| title_full_unstemmed | Valid and efficient entanglement verification with finite copies of a quantum state |
| title_short | Valid and efficient entanglement verification with finite copies of a quantum state |
| title_sort | valid and efficient entanglement verification with finite copies of a quantum state |
| url | https://doi.org/10.1038/s41534-024-00810-3 |
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